Introduction and Related Works

Perhaps the main improvement in the MAC protocol design was the intro-duction of carrier sense multiple access (CSMA) technique by Kleinrock and Tobagi [30]. The terminology hcarriersensei does not necessarily imply the use of a carrier, but simply the ability to quickly detect use of the chan-nel. CSMA reduces the level of interference (caused by overlapping packets) in the random multi-access environment by allowing terminals to sense the carrier due to other users’ transmissions; based on this channel state informa-tion (busy or idle), the terminal takes an acinforma-tion prescribed by the particular CSMA protocol being used (persistent, non-persistent, etc). In particular, a terminal never transmits when it senses that the channel is busy. In single-hop networks where all terminals share the same channel (carrier sense is efficient) CSMA protocols may achieve very good performances if the re-transmission scheme is well designed.

In the popular, and widely used IEEE802.11 standard for WLANs [13], the primary medium access control (MAC) technique is called distributed coor-dination function (DCF). DCF is a carrier sense multiple access with

colli-sion avoidance (CSMA/CA) scheme and slotted binary exponential backoff (BEB) rules. Since the introduction of the standard, many works have been interested in the analytical evaluation of its performance; most of them were based on the model of Bianchi, [31], and consider saturation throughput and delay analysis ( [32–34] to cite few). In real networks, packets may be queued at node’s buffer before being handled by the MAC protocol, and typical data traffics are bursty or streamed at low rates so that stations do note operate usually in saturated regime. Recent works have addressed the finite load per-formance of IEEE802.11 DCF with queueing at node’s (queues with infinite capacity) [35, 36] or with simplifying assumptions [37].

The analysis of queueing model of MAC protocols is a challenging task, and generally does not permit to obtain closed-form expressions of quantities of interest. In this work, we use a two-stage technique to analyze a queuing model of DCF protocol. In order to acquire closed-form expression of system performance, a Markov chain model is first used to analyze the non-queueing operation of the system. The traffic load in this case is modeled as a proba-bility of having a packet to transmitq, this probability is taken into account whenever the protocol is able to handle a new packet. In this way, q al-lows us to consider the fact that packet arrivals may occur anytime during the operation of the system. From the non-queueing model, we obtain the service-time statistics corresponding to a given q. In the second phase, we consider a queueing model of the system with a given arrival process λ(t) and queue lengthK. Thus, the probability of having a packet to transmitq corresponds to the probability q0 of having at least one packet in the queue.

In order to link the two models, we use a recursive algorithm that updates the q value used in the Markov model to specify the service time statistics, to match the resulting q0 from the queueing model.

It is well recognized that the key optimization issue of random access proto-cols is the design of an optimal retransmission scheme that keeps access rate to the multiple-access channel around its capacity. Obviously, an optimal retransmission scheme must achieve this capacity under all network condi-tions and must be distributed. The optimality of the scheme depends on how accurate is the information it has about the multiple access channel state.

IEEE802.11 DCF uses a BEB retransmission scheme. The BEB scheme has the advantage of being simple and does not require cooperation among users or any information about the channel state, it tries to blindly adapt the con-tention window to the channel congestion level based only on its experience, i.e., the contention window is increased in case of collision and it is reset to

3.1 Introduction and Related Works 45 its initial value in case of success. Its performances however are shown to be sub-optimal, in term of the achieved throughput as it needs several at-tempts to find approximately the best contention window, and also in term of short-term fairness as it favors the first successful user to compete again for the channel with small contention window against potentially others users with much higher contention window. Works in [38, 39] have derived specific fairness metric to illustrate this.

The enhancement of the DCF based BEB have been extensively addressed in the literature, the proposed schemes may be categorized into two classes:

1. Fully blind schemes: as in BEB, the change of the contention window’s length is made upon collision or success but in a different manner than BEB (MILD [40], FCR [41], EIED [42] to cite few) in order to better reach the optimal backoff window and/or increase short-term fairness.

2. coherent schemes: here the optimization is made in order to dynam-ically adapt the contention window to meet directly some objective optimization condition. The objective condition is derived from an an-alytical model and its verification is made by measuring (estimating) some specific performance metrics, [43–46] to site few. Even if these schemes identify and try to reach an optimal operating point of the system, the way they update the backoff window is not optimal as in the blind schemes.

Early in the work of Bianchi [31], the notion of optimal backoff window that optimizes the saturation network throughput has been introduced. Unfor-tunately, the calculation of this optimal window requires information about the network size N and the average duration of collisions E[Tcol]. Even if N could be easily obtained in single-hop network, channel activity sensing is required to estimate E[Tcol] in case of heterogeneous network where users employ different physical rates and/or packet sizes.

As DCF provides equal long-term access rate to different users, several stud-ies have shown that it is unable to fairly and efficiently manage heterogeneous networks [36, 43, 47–50]. As solution, time-based scheduling that guarantee equal channel time access to different users have been shown to increase both the throughput and fairness of the MAC protocol [48].

In order to achieve trivially time-based scheduling with DCF, it is sufficient to normalize the packet duration by normalizing the packet-size/physical-rate ratio, i.e., each physical packet-size/physical-rate is to be used with a corresponding packet

size in order to get unique packet duration on the channel and hence, a priori, fair input to the system. In this case, we can implement the optimal-window backoff scheme of [31] without estimating E[Tcol].

3.1.1 Contribution

In this chapter, we consider backoff-window optimization issue of finite load single-hop networks based on the idea in [31]. In order to avoid estimat-ing collision durations, we suppose that packet durations are normalized.

Obviously, the optimal backoff-window in this case will depend also on the traffic load. However, we will show that is sufficient to use the saturation’s optimal window under all loads to achieve nearly the maximum achievable throughput. Our main contributions are:

• New analytical model to consider finite load performance of DCF with-out queueing at nodes buffers.

• Proof of the short term unfairness of the binary exponential scheme by using channel capture probability as fairness metric.

• Accurate delay statistics model considering self-loop probability on every backoff state.

• Derivation of the contention window size for the optimal constant-window backoff (OCB) scheme. The optimal constant-window is achieved only for arrival rates greater than a specific threshold (saturation regime), below this threshold the optimal window is simply of length 2. How-ever, we prove in this work that the saturation optimal window is quasi-optimal under all traffic loads.

• Deep analysis of the operations of the BEB and OCB schemes with respect to load variations using numerical results. We show that OCB performs better than BEB, in term of throughput, delay, and fairness, while remaining quasi-insensitive to traffic load.

• Analytical model to consider finite queuing capacity of nodes based on the delay statistics model of the non-queueing model. Using results on M/G/1/K queues, we will use a recursive algorithm to link the delay statistics produced by a given traffic load to a corresponding arrival process (Markovian in our case) and queue length.